POWELLZLATNI

%POWELL SA ZLATNIM
function [ x,fx ] = p( fun,x0,tol )
%P Summary of this function goes here
%   Detailed explanation goes here
n = length(x0);
e = eye(n);
x = x0; t = x0 + 2*tol;
while abs(t - x) > tol
    x = t;
    for i = 1 : n
        g = @(k) t + k*e(:,i);
        c = @(j) fun(g(j));
        teta = z(c,-10,10,tol);
        t = t + teta * e(:,i);
    end
    e = [e(:,2:n) t-x];
    g = @(k) t + k*e(:,i);
    c = @(j) fun(g(j));
    teta = z(c,-10,10,tol);
    t = t + teta * e(:,i);
end
x = t;
fx = feval(fun,x);


%ZLATNI
function [ x ] = z( fun,a,b,tol )
%Z Summary of this function goes here
%   Detailed explanation goes here
    c = (3 - sqrt(5) )/ 2;
    x1 = a + c*(b-a);
    x2 = a + b - x1;

    while (b - a) > tol
        if feval(fun,x1) > feval(fun,x2)
            a = x1;
            x1 = x2;
            x2 = a + b - x1;
        else
            b = x2;
            x2 = x1;
            x1 = a + b - x2;
        end
    end
    if feval(fun,x1) < feval(fun,x2)
        x = x1;
    else
        x = x2;
    end
end